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Chapter 2: Q52P-a (page 45)
In the circuit shown in Figure 19.75, the emf of the battery is . Resistor has a resistance of , and resistor has a resistance of . A steady current flows through the circuit. (a) What is the absolute value of the potential difference across ? (b) What is the conventional current through ?
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In a crash test, a truck with mass 2500kgtraveling at 24m/ssmashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck is 0.72mshorter than before,
(a) What is the average speed of the truck during the collision (that is, during the interval between first contact with the wall and coming to a stop)?
(b) About how long does the collision last? (That is, how long is the interval between first contact with the wall and coming to a stop?)
(c) What is the magnitude of the average force exerted by the wall on the truck during the collision?
(d) It is interesting to compare this force to the weight of the tuck. Calculate the ratio of the force of the wall to the gravitational forceon the truck. This large ratio shows why a collision is so damaging.
(e) What approximations did you make in your analysis?
A tennis ball has a mass of 0.057kg.A professional tennis player hits the ball hard enough to give it a speed of 50 m/s (about 120 mi/h). The ball hits a wall and bounces back with almost the same speed (50m/s). As indicated in Figure 2.55 , high-speed photography shows that the ball is crushed 2 cm (0.02 m) at the instant when its speed is moment0arily zero, before rebounding.
Making the very rough approximation that the large force that the wall exerts on the ball is approximately constant during contact, determine the approximate magnitude of this force. Hint: Think about the approximate amount of time it takes for the ball to come momentarily to rest. (For comparison note that the gravitational force on the ball is quite small, only about (0.057 kg) (9.8 N/kg) N. A force of5N is approximately the same as a force of one pound.)
You throw a metal block of mass \(0.25\;\;{\rm{kg}}\)into the air, and it leaves your hand at time\(t = 0\)at location\(\langle 0,2,0\rangle \;{\rm{m}}\)with velocity\(\langle 3,4,0\rangle \;{\rm{m}}/{\rm{s}}\). At this low velocity air resistance is negligible. Using the iterative method shown in Section\(2.4\)with a time step of\(0.05\;\;{\rm{s}}\),calculate step by step the position and velocity of the block at\(t = 0.05\;\;{\rm{s}},t = 0.10\;\;{\rm{s}}\), and\(t = 0.15\;\;{\rm{s}}\)
You observe three carts moving to the left. Cart A moves to the left at nearly constant speed. Cart B moves to the left, gradually speeding up. Cart C moves to the left, gradually slowing down. Which cart or carts, if any, experience a net force to the left?
A paddle ball toy consists of a flat wooden paddle and asmall rubber ball that are attached to each other by an elastic band (Figure 2.61). You have a paddle ball toy for which the mass of the ball is 0.015 kg, the stiffness of the elastic band is 0.9 N/m, and the relaxed length of the elastic band is 0.30 m. You are holding the paddle so the ball hangs suspended under it, when your cat comes along and bats the ball around, setting it in motion. At a particular instant the momentum of the ball is , and the moving ball is at location relative to an origin located at the point where the elastic band is attached to the paddle.
(a) Determine the position of the ball 0.1 s later, using of 0.1 s.
(b) Starting with the same initial position
and momentum , determine the position of the ball 0.1 s later, using a of 0.05 s. (c) If your answers are different, explain why.
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